TITLE:
On Subsets of Q(√m) Q under the Action of Hecke Groups H(λq)
AUTHORS:
M. Aslam Malik, M. Asim Zafar
KEYWORDS:
Quadratic Irrationals, Hecke Groups, Legendre Symbol, G-Set
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.8,
May
15,
2014
ABSTRACT: is the
disjoint union of for
all , where is the
set of all roots of primitive second degree equations , with reduced discriminant equal
to k2m. We study the action of two Hecke groups—the full modular group and
the group of linear-fractional transformations on . In particular, we investigate the action of on for
finding different orbits.